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2 years ago

If the measure of angle 4 is 11x and angle 3 is 4x , what is the measure of angle 3 in degrees?

1 answer:

5 0

Answer:
Let x = degree measure of the angle
So, the complement of the angle has degree measure 90-x
4/11 = x/(90-x)
4(90-x) = 11x
360 - 4x = 11x
15x = 360
x = 24°
Supplement = 180 - x = 156° x/(180-x) = 24/156 = 2/13

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The profile of the cables on a suspension bridge may be modeled by a parabola. The central span of the bridge is 1210 m long and

brilliants [131]

Answer:

The approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.

Step-by-step explanation:

The equation of the parabola is:

$y=0.00035x^{2}$

Compute the first order derivative of y as follows:

$y=0.00035x^{2}$

$\frac{\text{d}y}{\text{dx}}=\frac{\text{d}}{\text{dx}}[0.00035x^{2}]$

$=2\cdot 0.00035x\\\\=0.0007x$

Now, it is provided that |x | ≤ 605.

⇒ -605 ≤ x ≤ 605

Compute the arc length as follows:

$\text{Arc Length}=\int\limits^{x}_{-x} {1+(\frac{\text{dy}}{\text{dx}})^{2}} \, dx$

$=\int\limits^{605}_{-605} {\sqrt{1+(0.0007x)^{2}}} \, dx \\\\={\displaystyle\int\limits^{605}_{-605}}\sqrt{\dfrac{49x^2}{100000000}+1}\,\mathrm{d}x\\\\={\dfrac{1}{10000}}}{\displaystyle\int\limits^{605}_{-605}}\sqrt{49x^2+100000000}\,\mathrm{d}x\\\\$

Now, let

$x=\dfrac{10000\tan\left(u\right)}{7}\\\\\Rightarrow u=\arctan\left(\dfrac{7x}{10000}\right)\\\\\Rightarrow \mathrm{d}x=\dfrac{10000\sec^2\left(u\right)}{7}\,\mathrm{d}u$

$\int dx={\displaystyle\int\limits}\dfrac{10000\sec^2\left(u\right)\sqrt{100000000\tan^2\left(u\right)+100000000}}{7}\,\mathrm{d}u$

$={\dfrac{100000000}{7}}}{\displaystyle\int}\sec^3\left(u\right)\,\mathrm{d}u\\\\=\dfrac{50000000\ln\left(\tan\left(u\right)+\sec\left(u\right)\right)}{7}+\dfrac{50000000\sec\left(u\right)\tan\left(u\right)}{7}\\\\=\dfrac{50000000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+5000x\sqrt{\dfrac{49x^2}{100000000}+1}$

Plug in the solved integrals in Arc Length and solve as follows:

$\text{Arc Length}=\dfrac{5000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+\dfrac{x\sqrt{\frac{49x^2}{100000000}+1}}{2}|_{limits^{605}_{-605}}\\\\$

$=1245.253707795227\\\\\approx 1245.25$

Thus, the approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.

7 0

2 years ago

30 POINTS !! PLEASE HELP ASAP!!

inn [45]

Answer: a) 4 b) Bachelor’s

Steps:
1000 * 4%
1000 * 0.04
40

1000 + x = 1160
x = 160

160 / 40 = 4

Went to school for 4 years

A 4 year college degree is a bachelor’s degree

3 0

2 years ago

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Math help j: pls Heh

BabaBlast [244]

Answer:

7/10

Step-by-step explanation:

0.7+0.07+0.007=0.777

fraction=777/1000

simplest form: 777/1000=7/10

srry if im wrong

hope this helps :3

8 0

2 years ago

Suppose that 5 t shirts cost $55 what's the unit rate?

Kamila [148]

$55 / 5 =$11

unit rate $11

answer
$11 per shirt

5 0

2 years ago

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What is the solution to the linear equation? 4b + 6 = 2 – b + 4

Reil [10]

Answer:

$\large\boxed{b=0}$

Step-by-step explanation:

$4b+6=2-b+4\qquad\text{combine like terms}\\\\4b+6=(2+4)-b\qquad\text{add}\ b\ \text{to both sides}\\\\5b+6=6\qquad\text{subtract 6 from both sides}\\\\5b=0\qquad\text{divide both sides by 5}\\\\b=0$

8 0

2 years ago

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